A038050 Number of labeled rooted trees with 3-colored leaves.

3, 6, 45, 504, 7785, 153468, 3681909, 104126256, 3392064945, 125089571700, 5151335388309, 234322765501608, 11668410187187481, 631335472193760012, 36881146426978035765, 2313552152470193124192, 155107536736245864549345

Offset

1,1

References

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.83)

Links

Table of n, a(n) for n=1..17.

Index entries for sequences related to rooted trees

N. J. A. Sloane, Transforms

Formula

Divides by n and shifts left under exponential transform.

E.g.f.: 2*x - LambertW(-x*exp(2*x)). - Vladeta Jovovic, Mar 09 2003

a(n) = Sum_{k=0..n} (binomial(n, k)*2^k*(n-k)^(n-1)).

a(n) ~ sqrt(1+LambertW(2*exp(-1))) * (2*exp(-1)/LambertW(2*exp(-1)))^n * n^(n-1). - Vaclav Kotesovec, Oct 05 2013

Mathematica

Rest[CoefficientList[Series[2*x-LambertW[-x*E^(2*x)], {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Oct 05 2013 *)

Crossrefs

Cf. A000169, A029857.

Cf. A038049.

Sequence in context: A203434 A076170 A137775 * A194080 A261841 A197884

Adjacent sequences: A038047 A038048 A038049 * A038051 A038052 A038053

Keyword

nonn,eigen

Author

Christian G. Bower, Jan 04 1999

Status

approved